[itex]\beta_i [/itex] being [itex]\beta n_i [/itex], and [itex]\sigma^i \sigma^\mu \sigma_i [/itex] coming from [itex](\vec{\sigma} \cdot \vec{n}) \sigma^\mu (\vec{\sigma} \cdot \vec{n})[/itex] (I can't find the exact proof to show it to be so, but I think this is correct - though it may be the problem). So far this is pretty much the results indicated. But then, if I try finding out the results using this identity :